A two- or three-dimensional contour has hitherto been machined electroerosively in a workpiece by preparing a tool electrode so shaped as to be complementary with the desired contour and advancing or "sinking" the tool electrode in a given direction progressively into the workpiece while an electroerosion machining current is passed between the tool electrode and the workpiece. An intricate contour may also be machined electroerosively in a workpiece with a simple solid electrode by controlling machining feed to displace the tool electrode relative to the workpiece along a sequence of displacement paths. In this latter process, the tool electrode need not be shaped to be complementary to the desired two- or three-dimensional contour and the workpiece is supported on a movable worktable to lie in a horizontal or X-Y plane. During the machining operation, the worktable is driven horizontally to displace the workpiece along X- and Y-coordinate axes or, further, vertically to displace the workpiece along a Z-coordinate axis orthogonal to the X-Y plane, relative to the tool electrode fixed in position, so that the desirable two- or three-dimensional contour determined by eventual paths of relative displacement is formed in the workpiece. While this process in eliminating the need for the laborious, time-consuming and costly job of shaping a particular electrode tool complementary to each individual contour desired, offers greater advantages over the sinking-type process, it has been found to be often defective in achieving the desired contour with due precision and finish, especially at corner or angular portions thereof, thus necessitating a further finishing operation with a replaced electrode tool.